Approximation Benefits of Policy Gradient Methods with Aggregated States
This provides theoretical justification for the robustness of policy gradient methods in reinforcement learning with state aggregation, which is incremental but clarifies a known bottleneck.
The paper tackles the problem of policy gradient methods being more robust to approximation errors in state-aggregated representations compared to approximate policy iteration and value iteration, showing that policy gradient converges with per-period regret bounded by ε, while the others scale as ε/(1-γ).
Folklore suggests that policy gradient can be more robust to misspecification than its relative, approximate policy iteration. This paper studies the case of state-aggregated representations, where the state space is partitioned and either the policy or value function approximation is held constant over partitions. This paper shows a policy gradient method converges to a policy whose regret per-period is bounded by $ε$, the largest difference between two elements of the state-action value function belonging to a common partition. With the same representation, both approximate policy iteration and approximate value iteration can produce policies whose per-period regret scales as $ε/(1-γ)$, where $γ$ is a discount factor. Faced with inherent approximation error, methods that locally optimize the true decision-objective can be far more robust.